Problem: Simplify the following expression: $\sqrt{3}+\sqrt{75}+\sqrt{12}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{3}+\sqrt{75}+\sqrt{12}$ $= \sqrt{3}+\sqrt{25 \cdot 3}+\sqrt{4 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{3}+\sqrt{25} \cdot \sqrt{3}+\sqrt{4} \cdot \sqrt{3}$ $= \sqrt{3}+5\sqrt{3}+2\sqrt{3}$ Finally, simplify by combining the terms. $= ( 1 + 5 + 2 )\sqrt{3} = 8\sqrt{3}$